If she agrees to the move, it would see Pussycat Dolls singer Nicole Scherzinger – who was given Cheryl’s place on the panel after her sudden exit – relegated to her original role as co-host with British TV pre¬senter Steve Jones.

But there was speculation the offer could be a plot by the American TV network to stave off any legal claim that Miss Cole could make for compensation against her sacking.

She was expected to receive a £1.2million payout in compensation despite filming only four episodes of the £100million series. However, if she then chooses not to accept Fox’s offer, it could reduce any payment the network would have to pay out.

Last night a spokesman for Miss Cole did not return calls.

A judge or co-host? Cheryl's return will mean Scherzinger - who performed on Britain's Got Talent last night - will revert to presenting

Miss Cole, one of four judges on the panel alongside Cowell, Paula Abdul and record producer L. A. Reid, flew back to Britain two weeks ago.

No official explanation has yet emerged as to why Miss Cole was dropped and sources close to her said she was not told why.

However, Fox executives were said to have complained about the ‘lack of chemistry’ between her and fellow judge Miss Abdul and concerns were raised about Miss Cole’s accent.

She was also criticised for her fashion sense and hairstyle after she arrived for her first day on the panel in purple trousers, an orange top and a backcombed hairstyle which Simon Cowell later said looked as if it was created in a wind tunnel.

Last week, British television executives gave Miss Cole the chance to resume her place on the ITV show – but she declined their offer after failing to respond to a deadline set for midnight last Saturday.

A source close to Cowell said last night: ‘Simon is staying out of this now. He has offered an olive branch but he is leaving the decisions up to Fox and Freemantle, the production company.

New panel: Louis Walsh is joined by Kelly Rowland, Tulisa Contostavlos and Gary Barlow at the Birmingham auditions of X Factor last week

‘Cheryl was offered the UK show because it was thought that would have made her happier. He just wants whatever is best for Cheryl.’

Her U.S. manager, Black Eyed Peas rapper Will.i.am said last week: 'Cheryl always comes back stronger, and she always comes back bigger. Cheryl has been through rougher things than this, so this is going to be no problem for her.

'It's easy to imagine Simon as this one-man empire, but that's not the case.

'He has people he needs to answer to and sometimes his hands are tied. I can only tell you what I've seen first-hand, that's a guy who deeply cares for her.'

The latest development comes just a few days after it was confirmed Mrs Cole would not be returning to the original UK X Factor.

Instead Gary Barlow, Tulisa Contostavlos and Kelly Rowland joined the only remaining judge Louis Walsh on the panel at the Birmingham auditions last week.

Walsh said he had spoken to Cole and she was doing 'fine'.

He said: 'I talked to Cheryl today - we’ve been texting all day and we’re having fun. I think she’s going to be fine.